On the Merit of Selecting Different Belief Merging Operators

Belief merging operators combine multiple belief bases (a profile) into a collective one. When the conjunction of belief bases is consistent, all the operators agree on the result. However, if the conjunction of belief bases is inconsistent, the results vary between operators. There is no formal manner to measure the results and decide on which operator to select. So, in this paper we propose to evaluate the result of merging operators by using three ordering relations (fairness, satisfaction and strength) over operators for a given profile. Moreover, a relation of conformity over operators is introduced in order to classify how well the operator conforms to the definition of a merging operator. By using the four proposed relations we provide a comparison of some classical merging operators and evaluate the results for some specific profiles.

A comparison of merging operators in possibilistic logic.

In this paper, we compare merging operators in possibilistic logic. We rst propose an approach to evaluating the discriminating power of a merging operator. After that, we analyze the computational complexity of existing possibilistic merging operators. Finally, we consider the compatibility of possibilistic merging operators with propositional merging operators.

Belief change with noisy sensing in the situation calculus

Situation calculus has been applied widely in arti?cial intelligence to model and reason about actions and changes in dynamic systems. Since actions carried out by agents will cause constant changes of the agents’ beliefs, how to manage
these changes is a very important issue. Shapiro et al. [22] is one of the studies that considered this issue. However, in this framework, the problem of noisy sensing, which often presents in real-world applications, is not considered. As a
consequence, noisy sensing actions in this framework will lead to an agent facing inconsistent situation and subsequently the agent cannot proceed further. In this paper, we investigate how noisy sensing actions can be handled in iterated
belief change within the situation calculus formalism. We extend the framework proposed in [22] with the capability of managing noisy sensings. We demonstrate that an agent can still detect the actual situation when the ratio of noisy sensing actions vs. accurate sensing actions is limited. We prove that our framework subsumes the iterated belief change strategy in [22] when all sensing actions are accurate. Furthermore, we prove that our framework can adequately handle belief introspection, mistaken beliefs, belief revision and belief update even with noisy sensing, as done in [22] with accurate sensing actions only.

Norms of basic elementary operators on algebras of regular operators

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r||B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.

Generating analysis topology using virtual topology operators

Virtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities, where virtual decompositions are robustly linked to the underlying geometry. Current virtual topology technology is extended to allow the virtual partitioning of volume cells. A valid description of the topology, including relative orientations, is maintained which enables downstream interrogations to be performed on the analysis topology description, such as determining if a specific meshing strategy can be applied to the virtual volume cells. As the virtual representation is a true non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. Therefore, the advantages of non-manifold modelling are exploited within the manifold modelling environment of a major commercial CAD system without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies here are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence.

Operators for Similarity Search: Semantics, Techniques and Usage Scenarios

This book provides a comprehensive tutorial on similarity operators. The authors systematically survey the set of similarity operators, primarily focusing on their semantics, while also touching upon mechanisms for processing them effectively.

The book starts off by providing introductory material on similarity search systems, highlighting the central role of similarity operators in such systems. This is followed by a systematic categorized overview of the variety of similarity operators that have been proposed in literature over the last two decades, including advanced operators such as RkNN, Reverse k-Ranks, Skyline k-Groups and K-N-Match. Since indexing is a core technology in the practical implementation of similarity operators, various indexing mechanisms are summarized. Finally, current research challenges are outlined, so as to enable interested readers to identify potential directions for future investigations.

In summary, this book offers a comprehensive overview of the field of similarity search operators, allowing readers to understand the area of similarity operators as it stands today, and in addition providing them with the background needed to understand recent novel approaches.

A study of singular integral operators with shift

Nesta tese, consideram-se operadores integrais singulares com a acção extra de um operador de deslocacamento de Carleman e com coeficientes em diferentes classes de funções essencialmente limitadas. Nomeadamente, funções contínuas por troços, funções quase-periódicas e funções possuíndo factorização generalizada. Nos casos dos operadores integrais singulares com deslocamento dado pelo operador de reflexão ou pelo operador de salto no círculo unitário complexo, obtêm-se critérios para a propriedade de Fredholm. Para os coeficientes contínuos, uma fórmula do índice de Fredholm é apresentada. Estes resultados são consequência das relações de equivalência explícitas entre aqueles operadores e alguns operadores adicionais, tais como o operador integral singular, operadores de Toeplitz e operadores de Toeplitz mais Hankel. Além disso, as relações de equivalência permitem-nos obter um critério de invertibilidade e fórmulas para os inversos laterais dos operadores iniciais com coeficientes factorizáveis. Adicionalmente, aplicamos técnicas de análise numérica, tais como métodos de colocação de polinómios, para o estudo da dimensão do núcleo dos dois tipos de operadores integrais singulares com coeficientes contínuos por troços. Esta abordagem permite também a computação do inverso no sentido Moore-Penrose dos operadores principais. Para operadores integrais singulares com operadores de deslocamento do tipo Carleman preservando a orientação e com funções contínuas como coeficientes, são obtidos limites superiores da dimensão do núcleo. Tal é implementado utilizando algumas estimativas e com a ajuda de relações (explícitas) de equivalência entre operadores. Focamos ainda a nossa atenção na resolução e nas soluções de uma classe de equações integrais singulares com deslocamento que não pode ser reduzida a um problema de valor de fronteira binomial. De forma a atingir os objectivos propostos, foram utilizadas projecções complementares e identidades entre operadores. Desta forma, as equações em estudo são associadas a sistemas de equações integrais singulares. Estes sistemas são depois analisados utilizando um problema de valor de fronteira de Riemann. Este procedimento tem como consequência a construção das soluções das equações iniciais a partir das soluções de problemas de valor de fronteira de Riemann. Motivados por uma grande diversidade de aplicações, estendemos a definição de operador integral de Cauchy para espaços de Lebesgue sobre grupos topológicos. Assim, são investigadas as condições de invertibilidade dos operadores integrais neste contexto.

Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.

Symmetric quantum calculus

Generalizamos o cálculo Hahn variacional para problemas do cálculo das variações que envolvem derivadas de ordem superior. Estudamos o cálculo quântico simétrico, nomeadamente o cálculo quântico alpha,beta-simétrico, q-simétrico e Hahn-simétrico. Introduzimos o cálculo quântico simétrico variacional e deduzimos equações do tipo Euler-Lagrange para o cálculo q-simétrico e Hahn simétrico. Definimos a derivada simétrica em escalas temporais e deduzimos algumas das suas propriedades. Finalmente, introduzimos e estudamos o integral diamond que generaliza o integral diamond-alpha das escalas temporais.

Calculus of variations on time scales and applications to economics

We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.

Mathematica in the classroom: new tools for exploring precalculus and differential calculus

Prémio de Melhor Artigo de Jovem Investigador atribuído pela empresa Timberlake, apresentado na 1ª Conferência Nacional sobre Computação Simbólica no Ensino e na Investigação - CSEI2012, que decorreu no IST nos dias 2 e 3 de Abril.